Related papers: Verifying term graph optimizations using Isabelle/…
Interactive theorem provers, like Isabelle/HOL, Coq and Lean, have expressive languages that allow the formalization of general mathematical objects and proofs. In this context, an important goal is to reduce the time and effort needed to…
Reusing verification artefacts requires identifying structural and semantic similarities across programs and their specifications. In this paper, we focus on graph construction as a foundational step toward this goal. We present a pipeline…
We introduce a new class of graph transformation systems in which rewrite rules can be guarded by universally quantified conditions on the neighbourhood of nodes. These conditions are defined via special graph patterns which may be…
Thanks to their linguistic capabilities, LLMs offer an opportunity to bridge the gap between informal mathematics and formal languages through autoformalization. However, it is still unclear how well LLMs generalize to sophisticated and…
Traditional optimizing compilers rely on rewrite rules to iteratively apply program transformations. This iterative approach hides optimization opportunities behind intermediate transformation steps. For instance, vectorization can only be…
Several popular language models represent local contexts in an input text $x$ as bags of words. Such representations are naturally encoded by a sequence graph whose vertices are the distinct words occurring in $x$, with edges representing…
In the Matrix approach to graph transformation we represent simple digraphs and rules with Boolean matrices and vectors, and the rewriting is expressed using Boolean operators only. In previous works, we developed analysis techniques…
Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…
Optimizing a stateful dataflow language is a challenging task. There are strict correctness constraints for preserving properties expected by downstream consumers, a large space of possible optimizations, and complex analyses that must…
Modern large language model-based reasoning systems frequently recompute similar reasoning steps across tasks, wasting computational resources, inflating inference latency, and limiting reproducibility. These inefficiencies underscore the…
Successful application of large language models (LLMs) to robotic planning and execution may pave the way to automate numerous real-world tasks. Promising recent research has been conducted showing that the knowledge contained in LLMs can…
We present a way to implement term rewriting on a GPU. We do this by letting the GPU repeatedly perform a massively parallel evaluation of all subterms. We find that if the term rewrite systems exhibit sufficient internal parallelism, GPU…
There are many evaluation strategies for term rewrite systems, but automatically proving termination or analyzing complexity is usually easiest for innermost rewriting. Several syntactic criteria exist when innermost termination implies…
Encodings of term rewriting systems (TRSs) into graph rewriting systems usually lose global termination, meaning the encodings do not terminate on all graphs. A typical encoding of the terminating TRS rule a(b(x)) -> b(a(x)), for example,…
Simple conceptual graphs are considered as the kernel of most knowledge representation formalisms built upon Sowa's model. Reasoning in this model can be expressed by a graph homomorphism called projection, whose semantics is usually given…
The security provided by a firewall for a computer network almost completely depends on the rules it enforces. For over a decade, it has been a well-known and unsolved problem that the quality of many firewall rule sets is insufficient.…
Formal verification via interactive theorem proving is increasingly used to ensure the correctness of critical systems, yet constructing large proof scripts remains highly manual and limits scalability. Advances in large language models…
Egel is an untyped eager combinator toy language. Its primary purpose is to showcase an abstract graph-rewriting semantics allowing a robust memory-safe construction in C++. Though graph rewriters are normally implemented by elaborate…
Linear programming describes the problem of optimising a linear objective function over a set of constraints on its variables. In this paper we present a solver for linear programs implemented in the proof assistant Isabelle/HOL. This…
Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal…